Rewrite as a simplified fraction. ${0.6\overline{47} = {?}}$
Let $x$ equal the decimal. Set up two equations such that the digits after the decimal point are identical. ${\begin{align*}1000x &= 647.4747...\\ 10x &= 6.4747...\end{align*}}$ Subtracting the two equations, we have: ${990x = 641}$ ${x = \dfrac{641}{990}} $